# Single Machine Preemptive Scheduling to Minimize the Weighted Number of Late Jobs with Deadlines and Nested Release/Due Date Intervals

Valery S. Gordon; F. Werner; O. A. Yanushkevich

RAIRO - Operations Research (2010)

- Volume: 35, Issue: 1, page 71-83
- ISSN: 0399-0559

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topGordon, Valery S., Werner, F., and Yanushkevich, O. A.. "Single Machine Preemptive Scheduling to Minimize the Weighted Number of Late Jobs with Deadlines and Nested Release/Due Date Intervals." RAIRO - Operations Research 35.1 (2010): 71-83. <http://eudml.org/doc/197794>.

@article{Gordon2010,

abstract = {
This paper is devoted to the following version of the single machine
preemptive scheduling problem of minimizing the weighted number of late
jobs. A processing time, a release date, a due date and a weight of each
job are given. Certain jobs are specified to be completed in time, i.e.,
their due dates are assigned to be deadlines, while the other jobs are
allowed to be completed after their due dates. The release/due date
intervals are nested, i.e., no two of them overlap (either they have at most
one common point or one covers the other).
Necessary and sufficient conditions for the completion of all jobs in time
are considered, and an
O(nlogn) algorithm (where n is
the number of jobs) is proposed for solving the problem of minimizing
the weighted number of late jobs in case of oppositely ordered processing
times and weights.
},

author = {Gordon, Valery S., Werner, F., Yanushkevich, O. A.},

journal = {RAIRO - Operations Research},

keywords = {Single machine scheduling; release and due dates;
deadlines; number of late jobs.; single machine scheduling; deadlines; number of late jobs},

language = {eng},

month = {3},

number = {1},

pages = {71-83},

publisher = {EDP Sciences},

title = {Single Machine Preemptive Scheduling to Minimize the Weighted Number of Late Jobs with Deadlines and Nested Release/Due Date Intervals},

url = {http://eudml.org/doc/197794},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Gordon, Valery S.

AU - Werner, F.

AU - Yanushkevich, O. A.

TI - Single Machine Preemptive Scheduling to Minimize the Weighted Number of Late Jobs with Deadlines and Nested Release/Due Date Intervals

JO - RAIRO - Operations Research

DA - 2010/3//

PB - EDP Sciences

VL - 35

IS - 1

SP - 71

EP - 83

AB -
This paper is devoted to the following version of the single machine
preemptive scheduling problem of minimizing the weighted number of late
jobs. A processing time, a release date, a due date and a weight of each
job are given. Certain jobs are specified to be completed in time, i.e.,
their due dates are assigned to be deadlines, while the other jobs are
allowed to be completed after their due dates. The release/due date
intervals are nested, i.e., no two of them overlap (either they have at most
one common point or one covers the other).
Necessary and sufficient conditions for the completion of all jobs in time
are considered, and an
O(nlogn) algorithm (where n is
the number of jobs) is proposed for solving the problem of minimizing
the weighted number of late jobs in case of oppositely ordered processing
times and weights.

LA - eng

KW - Single machine scheduling; release and due dates;
deadlines; number of late jobs.; single machine scheduling; deadlines; number of late jobs

UR - http://eudml.org/doc/197794

ER -

## References

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- J.B. Sidney, An extension of Moore's due date algorithm, edited by S.E. Elmaghraby, Symposium on the Theory of Scheduling and its Applications. Springer, Berlin, Lecture Notes in Econom. and Math. Systems86 (1973) 393-398. Zbl0273.90032
- V.S. Tanaev and V.S. Gordon, On scheduling to minimize the weighted number of late jobs. Vestsi Akad. Navuk Belarus Ser. Fizi.-Mat. Navuk6 (1983) 3-9 (in Russian).
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